The pseudo-conformal scenario is an alternative to inflation in which the early universe is approximately described by a conformal field theory in Minkowski space. Crucially, the cosmological background spontaneously breaks the flat space so(4,2) conformal algebra down to its so(4,1) de Sitter subalgebra, causing conformal-weight-0 fields to acquire a scale invariant spectrum of perturbations. This framework is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics.

We comment on a certain partially reduced phase space quantisation of general relativity conformally coupled to a scalar field, and its extension to standard model matter fields. The partially reduced phase space is reached by trading the Hamiltonian constraint for the generator of local conformal transformations on all phase space variables, inspired by the ideas of shape dynamics, and constructing conformally invariant connection variables. Furthermore, we review this trading of symmetries from the gauge fixing/unfixing perspective, which is dual to the concept of a linking theory.

I will describe an approach to the problem of time that uses dust as a time variable. The canonical theory is such that there is a true Hamiltonian with spatial diffeomorphisms as the only gauge symmetry. This feature, and the form of the Hamiltonian, suggest a model for non-perturbative quantum gravity that is computationally accessible using the formalism of loop quantum gravity.

We present a new model of inflation which does not rely on fundamental scalar fields. The theory is a conformally invariant gauge field theory minimally coupled to massless fermions. At the beginning of inflation, the conformal symmetry is dynamically broken by a BCS condensation of the fermions, leading to a spontaneously violation of conformal symmetry. A quasi de-Sitter inflationary regime is driven by the interaction between a homogenous plasma dynamo between the gauge, gravitational and condensate field. Unique observational consequences of this model are twofold : (1) The sourcin

I show how the local Lorentz and/or diffeomorphism invariances may be broken by a varying c, softly or harshly, depending on taste. Regardless of the fundamental implications of such dramas, these symmetry breakings may be of great practical use in cosmology. They may solve the horizon and flatness problems. A near scale-invariant spectrum of fluctuation may arise, even without inflation. Distinct imprints may be left, teaching us an important lesson: our foundations may be flimsier than we like to think.

New techniques for obtaining the complete set of analytic solutions of the usual cosmological equations continue to shed new light on various aspects of cosmology. This approach, which was developed with a locally Weyl invariant formulation of gravity in 3+1 dimensions, was inspired by the 2T-physics formulation of all physics in 4+2 dimensions.

The Conformal Method (as well as the closely related Conformal Thin Sandwich Method) has proven to be a very useful procedure both for constructing and for parametrizing solutions of the Einstein initial data constraint equations, for initial data sets with constant mean curvature (CMC). Is this true for non CMC data sets as well? After reviewing the CMC results, we discuss what we know and don't know about non CMC initial data sets and the effectiveness of the Conformal Method in handling them.

Evidence from several approaches to quantum gravity hints at the possibility that spacetime undergoes a "spontaneous dimensional reduction" at very short distances. If this is the case, the small scale universe might be described by a theory with two-dimensional conformal symmetry. I will summarize the evidence for dimensional reduction and indicate a tentative path towards using this conformal invariance to explore quantum gravity.